Mathematical instruments



Feb. 13, 1962 J. R. HoRToN MATHEMATICAL INSTRUMENTS 2 Sheets-Sheet 1 Filed June 26, 1958 ATTORNEYS Feb. 13, 1962 J. R. HoRToN MATHEMATICAL INSTRUMENTS 2 Sheets-Sheet 2 Filed June 26, 1958 INVENTOR Jasav A75( Ham/g,

BY #MAM ATTORNEYS the trigonometer.

United ,States Patent O MATHEMATICAL INSTRUMENTS Joseph R. Horton, 1201 Hiwassee Ave., Knoxville, Tenn.

Filed June 26, 1958, Ser. No. 744,731

4 Claims. (Cl. 23S-61) from ytime to time to enable the determination of trigonometric functions. These devices have never met with general acceptance, becauseof their complexity of construction and operation. Accordingly, it is an object of this invention to provide such a device, capable .of indicating the desired information, the structure and operationv of whichis simple.

Another object of this invention is to provide a device p which may be constructed in any desiredfsize to facilitate ,instruction in trigonometric functions and their inter-relation.

A further object isto provide a mathematical instrui' ment having the requisite accuracy, whose parts are easily produced, and the cost of which can be held to a desirably low figure.

A preferred embodiment of this invention accomplishes vthe afore-mentioned objects by means of a composite structure comprising a back member having thereupon scales indicating the angles andthe values of their trigonometric functions. yRotatably mounted over the back member is an elongated vector operable to correlate the angles and the values of their functions'. In order to correlate completely the angles with all of their functions, i an intersector member is pivotally attached to the vector and cooperates therewith in such fashion that by a single t setting of the vector to the desired angle, all six trigonometric funetions of the angle may be read from the vector and intersector positions.

This preferred embodiment of the invention is illustrated in the accompanying drawings, in which:

FIG. 1 isa top plan View of the trigonometer;

FIG. 2 is a cross section taken along the line 2-2 in FIG. 1; and

FIG. 3 is'an exploded perspective view showing the various parts of the trigonometer in their order of assembly.

Referring now to FIGS. Il to 3 of the drawings, the numeral 1 is used to indicate the back or base member of The back 1 is made of opaque material suitable for the engraving or printing thereupon of small figured scales such as in ordinary slide rules. The

, particular material used in the preferred embodiment is plastic. However, any other suitable material could well be substituted.

` The back 1 is of generally square configuration, except for one corner thereof which is formed in a 90 arc. X

= and Y axes are laid out on the back 1 with their interto 90 at the positive Y axis.

In the second quadrant formed by the intersecting axes, a 90 arc is drawn about the negative end of the X axis and terminates at the intersecting point of the X and Y axes. This arc is marked off in divisions with values which follow the cosine function, to form a cosine scale 3.

The third quadrant is provided with two 90 arcs, the

first of which has for its center the.'ifitersie'ctio'ri point c 3,021,058 Patented Feb. 13, 1962 rice of the X and Y axesy and forms a double scale 4 having values of the secant and cosecant functions. The second arc is tangent to the negative X and Y axes and has its center located on the line bisecting the third quadrant. This second arc forms another double scale .5 having values ,of the tangent and cotangent functions.

The fourth quadrant has a 90 arc drawn about the Ynegative end of the Y axis and terminating at the intersecting point of the X and Y axes. This arc is marked off in values of the sine function and forms a sine scale 6. Since the back 1 is opaqueand the back side thereof is entirely blank, additional formulae and tables may be printedon this space to be readily available and form-a liandy reference for the user.

' The straight edge portions of the back 1 are provided with small spaced holes 7 for assembly screws, bolts, etc., indicated at 7. Any other suitable fastening means may be used, Vas desired. There are no holes along the arc portion containing the degree scale 2 since this space must remain open.v f

Disposed over the back 1 is the vector 8. This member is a long narrow strip of transparent material, preferably of plastic, having a hair line 27 located centrally ,throughout its length; The vector 8 is provided with two small holes spaced along its central axis. The first of f these holes, 9, is located near the mid point of the vector,

while the second hole, 10, is located near one end. A linear scale 11 is provided along the hair line 27 between the holes 9 and 10. i'

The vector 8 is attached to the under side of vector -rnount 12,' the purpose kof which is to support the said vector. The vector mount 12 is similar in shape to the back 1, except that the arc portion of the first quadrant has ka smaller radius. The vector mount 12 is constructed'of transparent material, preferably plastic, and is also provided with similar spaced holes 7 .about the periphery, except along the arc portion of the first quadrant. Centrally located in the vector mount is a hole 13. A pin member 14 extends through the hole 13 of the vector mount and through the hole 9 of the vector,

to support these parts in pivotal relationship.

` Disposed between the back 1 and the vector mount 12 is' a vector spacer 15. This member is a narrow strip extending around the peripheral edges, with the exception of the arc portion as clearly shown in FIG. 3. The function of this vector spacer 15 is to mount the back 1 and jvector mount 12 in spaced relationship such that the vector 8' may freely rotate therebetween. Accordingly, the thickness of the vector spacer must be at least as great as the vector 8. The spacer 15, is also provided with small spaced holes 7 which are in alignment with intersector mount 16 is identical in shape to the vector mount 12, but the body portion thereof contains two smoothslots 17 and 18 of arcuate form which fit lin exact register over the scales 3 and 5 appearing on'the back 1 previously described.

An intersector 19 is a thin square of transparent material having linear scales 20 and 21 along two edges thereof and equipped with small depending pins 22, 23, 24, at three corners thereof. The pins 22 and 23 fit into ythe arcuate slots 17 and 18, respectively, in the intersector mount 16. Pin 24 fits into theL hole 10 in the vector 8 such lthat movementy of the vector 8 will cause a correspondingmovement ofthe intersector 1,9. t

" Disposed over theentire assembly is a cover member 25:whieh'ismade-'o'ftransparent-plasticmaterial and is 3 similar in shape to the vector mount 12 and the intersector mount 16. Spaced holes 7 are also provided about the peripheral edges of this member.

Located between the cover 25 and the intersector mount 16 is an intersector spacer 26. The intersector spacer 26 is identical in shape to the vector spacer 15, except that the ends bordering on the positive X and Y axes are slightly shorter. The intersector spacer 26 serves to hold the cover and intersector mount in spaced relationship such that the intersector 19 is free to move in the space therebetween.

The entire unit may be assembled by screws, rivets, or any other suitable fastening means 7 extending through the aligned spaced holes 7 located about the peripheries of the various component parts.

The operation of the trigonometer may be seen readily from FIG. 1. Movement of the vector 8 to any desired position on the degree scale 2 causes the intersector to change its position. The end of the vector opposite the degree scale 2 extends well into the third quadrant where the hair line 27 intersects the scale 4. Thus, the scales 3, 5, and 6, may be read from the positions of the three corners of the intersector 19, while the scales 2 and 4 may be read from the hair line 27 of the vector 8. The linear scales 20 and 21, together with the positive X and Y axes form with the hair line 27 triangles, the sides of which change in value with movement of the vector 8 to correspond with the trigonometric functions read from the various scales. Thus, in addition to reading the trigonometric function values from the scale, the linear values of the triangle sides may also be read, thus giving the student a pictorial correlation invaluable in establishing an understanding of the mathematical steps being studied.

With reference to FIG. l, the degree scale 2 will be graduated to 90 with the 0 mark appearing at the end of the positive X axis and the 90 mark appearing at the end of positive Y axis. The cosine scale 3 will be graduated 1 to 0 with the 1 mark appearing at the intersection of the X and Y axes. Similarly, the sine scale 6 will be graduated 1 to 0 with the 1 mark appearing at the intersection of the X and Y axes.

The tangent scale may be placed on either side of the double scale and will be graduated 0 to iniinity with the 0 mark appearing at the end of the negative X axis. The cotangent scale will be placed on the double scale 5 opposite the tangent scale and will be graduated 0 to infinity with the 0 mark appearing at the end of the negative Y axis.

The secant scale may -be placed on either side of the double scale 4 and will be graduated 1 to infinity with the 1 mark appearing at the end of the negative X axis. The cosecant scale will be placed on the double scale 4 opposite the secant scale and will be graduated 1 vto iniinity with the 1 mark appearing at the end of the negative Y axis.

For example, if the hair line 27 on the vector 8 is placed over the 45 mark on the degree scale 2 as shown approximately in FIG. 1, all of the trigonometric functions of a 45 angle can be read directly from the various scales. The upper left-hand corner of intersector 19 at 22l will indicate the cosine to be .707 on the cosine scale 3; the lower right-hand corner of the intersector 19 will indicate the sine to be .707 on the sine scale 6; the lower left-hand corner of the intersector 19 at 23 will indicate the tangent to be 1 and the contangent to be l on the double scale 5, and; the hair line Y2,'7 will indicate the secant to be 1.414 yand the cosecant to be 1.414 on the double scale 4.

The linear scales and 21 on the intersector 19 cross the positive Y and X axes, respectively, equal distances from ,the vintersection of the X and Y axes, as shown approximately in FIG. 1, thereby giving a pictorial represantatga gf a triangle. ,harias .equal ,sidesgppeste :and

adjacent the angle. The side adjacentthe angle is indicated on the positive X axis and the side opposite the angle is indicated on the positive Y axis. The triangle represented is formed by the positive X axis, the hair line 27, and the linear scale 21.

It will be apparent from this description that different arrangements of the parts are possible. For example, the vector 8 may be immediately below the cover Z5, while the intersector 19 may be placed immediately adjacent the back 1, where the vector 8 is now shown.

While the invention has been illustrated and described in one embodiment, it is recognized that variations and changes may be made therein without departing from the invention as set forth in the claims.

I claim:

1. In a device of the class described, a at base member having inscribed thereon intersecting X and Y axes forming quadrants; an elongated vector member of transparent material having a hair line running lengthwise thereof, said vector member being pivotally mounted with respect to said base member at the intersection of said X and Y axes and adapted to be grasped at one end and adjusted, an intersector member of substantially square configuration; means for pivotally connecting one corner of said intersector member with said vector member near the end of the vector member which is to be grasped; and means for mounting one of the remaining adjacent corners of said intersector member for guided arcuate movement with respect to said base member, the arc of said movement beginning at the intersection of said X and Y axes and having the end of one of said axes as the center thereof, pivotal movement of said vector member causing arcuate movement 0f each corner of said intersector member within one of the quadrants wherein the sides of said intersector member remain parallel to either said X or Y axis; said base member having inscribed thereon at least one arcuate scale aligned with the path followed by one of the remaining corners of said intersector member, and an arcuate scale near the end of the vector member which is to be grasped extending between the X and Y axes and having the intersection of said axes as the center thereof.

2. In a device of the class described, a at base member having inscribed thereon intersecting X and Y axes forming quadrants; a vector mount comprising a second iiat member of a shape generally similar to said base member; a spacer mem-ber between said vector mount and said 4base member for maintaining said vector mount and said base member is spaced-apart, parallel relationship; an elongated vector member of transparent material having a hair line running lengthwise thereof, said vector member being pivotally mounted on said vector mount opposite the intersection of said X and Y axes and adapted to be grasped at one end and adjusted; an intersector member of substantially square configuration; means for pivotally connecting one corner of said intersector member with said vector member near the end of the vector member which is to be grasped; and means for mounting one of the remaining adjacent corners of said intersector member for guided arcuate movement with respect to said base member, the arc of said movement beginning at the intersection of said X and Y axes and having the end of one of said axes as the center thereof, pivotal movement of said vector member causing arcuate movement of each corner of said intersector member within one of the quadrants wherein the sides of said intersector member remain parallel to either said X or Y axis; said base member having inscribed thereon at least one arcuate scale aligned with the path followed by one of the remaining corners of said intersector member, and an arcuate scale near the end of the vector member which is to be grasped extending between the X and Y axes and having the intersection of said axes as the center thereof.

3. In a device of the class described, a iiat base memb er having inscribed thereonintersecting X and Y axes forming quadrants; a vector mount comprising a second at member of a shape generally similar to said base mem-ber; a spacer member between said vector mount and said base member for maintaining said vector mount and said base member in spaced-apart, parallel relationship; an elongated vector member of transparent material having a hair line running lengthwise thereof, said vector mem-ber 'being pivotally mounted on said vector mount opposite the intersection of said X and Y axes and adapted to be grasped at one end and adjusted, an intersector mount comprising a third flat member of a shape similar to said vector mount; said intersector mount having an arcuate slot therein beginning at the intersection of said X and Y axes and having the end of one of said axes as the center thereof; an intersector member of substantially square configuration; means Ifor pivotally connecting one corner of said intersector member with said vector member near the end of the vector mem-ber which is to be grasped; a pin extending from one of the adjacent remaining corners of said intersector member and tting into the arcuate slot in said intersector mount -for guided movement therein, pivotal movement of said vector me'mber causing arcuate movement of each corner of said intersector member within one of the quadrants wherein the sides of said intersector member remain parallel to either said X or Y axis; said base member having inscribed thereon at least one arcuate scale aligned with the path followed by one of the remaining corners of said intersector member, and an arcuate scale near the end of the vector mem-ber which is to be grasped extending between the X and Y axes and having the intersection of said axes as the center thereof.

4. In a device of the class described, a flat base member having inscribed thereon intersecting X and Y axes forming quadrants; a vector mount comprising a second at member of a shape generally similar to said base member; a spacer member between said vector mount and said base member for maintaining said vector mount and said base member in spaced-apart, parallel relationship; an elongated vector member of transparent material having a hair line running lengthwise thereof, said vector member being pivotally mounted on said vector mount opposite the intersection of said X and Y axes and adapted to be grasped at one end and adjusted, an intersector mount comprising a third ilat member of a shape similar to said vector mount; said intersector mount having an arcuate slot therein beginning at the intersection of said X and Y axes and having the end of one of said axes as the center thereof; an intersector member of substantially square configuration; means for pivotally connecting one corner of said intersector member with said Vector'member near the end of the vector member which is to -be grasped; a pin extending from one of the adjacent remaining corners of said intersector mem-ber and fitting into the arcuate slot in said intersector mount for guided movement therein; pivotal movement of said vector member causin-g arcuate movement of each corner of said intersector member within one of the quadrants wherein the sides of said intersector member remain parallel to either said X or Y axis; said base member having inscribed thereon an arcuate scale in a rst quadrant near the end of the vector mem-ber which is to be grasped extending between the X and Y axes and having the intersection of said axes as the center thereof, arcuate scales in the three remaining quadrants each being aligned with the path followed =by one of the corners of said intersector member, and another arcuate scale in the quadrant opposite the rst quadrant extending between the X and Y axes and having the intersection of said axes as the center thereof.

References Cited in the le of this patent UNITED STATES PATENTS 

